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Mean, Median and Mode Calculator
Paste a list of numbers to find the mean, median, mode, range, quartiles and interquartile range in one step. The quartile method used is stated below so you can compare it with your textbook.
Three ways to find the centre of a list
The mean adds every value and divides by how many there are. The median is the middle value once the list is sorted; with an even count it is the average of the two middle values. The mode is the value that appears most often. A list can have one mode, several modes (when values tie for the highest count), or none at all when every value appears exactly once.
They answer different questions. The mean uses every value and is the natural choice for symmetric data. The median ignores how extreme the outer values are, so it is steadier when a few values are very large or very small. The mode is the only one of the three that also works for categories, though this page handles numbers only.
The quartile method used here
Quartiles split a sorted list into four parts, but textbooks and software do not all agree on how. This page uses the median-of-halves method: sort the list, split it into a lower and an upper half, leave out the middle value when the count is odd, and take the median of each half as Q1 and Q3. For 1 to 9 the lower half is 1, 2, 3, 4, so Q1 is 2.5, and the upper half is 6, 7, 8, 9, so Q3 is 7.5.
Spreadsheet functions often interpolate between positions instead and can return slightly different quartiles for the same list. Neither answer is wrong; they follow different conventions. If an assignment names a method, check that it matches this one.
Which measure to report
| Situation | Better measure |
|---|---|
| Roughly symmetric data without outliers | Mean |
| Skewed data such as incomes or house prices | Median |
| Finding the most common size or value | Mode |
| Describing spread that resists outliers | Interquartile range |
When the mean and median are far apart, the data is probably skewed or contains outliers. Reporting both tells the reader more than either alone.
Common mistakes
- Forgetting to sort before finding the median. The calculator sorts for you, but doing it by hand on an unsorted list gives the wrong middle.
- Calling the mode "zero" when nothing repeats. The correct statement is that there is no mode.
- Averaging averages. The mean of group means equals the overall mean only when the groups are the same size; use the average calculator with weights otherwise.
- Rounding too early. Keep full precision until the final answer.
Worked example
Nine daily step counts, in thousands: 12, 15, 11, 15, 18, 20, 15, 9, 11. Sorted, the middle (fifth) value is the median, and 15 appears three times.
Inputs
| Numbers | 12, 15, 11, 15, 18, 20, 15, 9, 11 |
|---|
Result
Mode: 15.
| Count | 9 |
|---|---|
| Sum | 126 |
| Mean | 14 |
| Median | 15 |
| Mode | 15 (appears 3 times) |
| Minimum | 9 |
| Maximum | 20 |
| Range | 11 |
| First quartile (Q1) | 11 |
| Third quartile (Q3) | 16.5 |
| Interquartile range (Q3 − Q1) | 5.5 |
| Sorted list | 9, 11, 11, 12, 15, 15, 15, 18, 20 |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How do I find the median of an even number of values?
Sort the list and average the two middle values. For 3, 5, 5, 7, 9, 10 the middle pair is 5 and 7, so the median is 6.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, all of them are modes. This calculator lists every one. If all values appear once, the set has no mode.
Why is my median different from the mean?
The mean is pulled toward extreme values while the median is not. A large gap between them usually signals skewed data or an outlier worth checking.
Why do my quartiles differ from my spreadsheet?
Several quartile conventions exist. This page takes the median of the lower and upper halves, excluding the middle value for odd counts. Spreadsheets often interpolate, which can give slightly different values.
How many numbers can I enter?
Up to 5,000, separated by commas, spaces or new lines. Decimals and negative numbers are accepted.
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References and sources
- NIST/SEMATECH e-Handbook of Statistical Methods: measures of location and quartiles. Link
- Tukey, J. W. (1977), Exploratory Data Analysis, for the hinge and median-of-halves approach to quartiles.